I do not want to say unplayable. I personally have never reached an unplayable stage. In the early days, when I first started playing the game, I would at times let it run overnight as I slept. There is no fear of doing this, since you can configure it to pause on events, such as war declarations. If you have a stable economy and are at peace, let it churn.
That being typed, I do not do that any longer as my play style has evolved. Now I am always here at the screen watching the world and trying to influence it as I would want it to be. 20, 50, 70 years in, the game is still playable. Now there are some things that greatly influence how this plays out.
In my opinion, the two largest issues being China and Russia. If they are taken out and those 1000's of units are removed from the game or even reserved, the game runs noticeably better.
Another issue is the settings you use, Fog of War, Line of Sight, etc. If I recall, the game is coded to have each unit check its field of view. Now, imagine, even though you may not be able to see all the units in the world, the game engine does and has to process every single one of them.
In my own experience there are 2 times a day when I can notice "lag/stutter/slowdown". At the bottom of the hour and at the top of the hour. Now, I am not computer literate at all, but just from observations I would guess the game checks units at the top of the hour and calculates the production side of things at the bottom. I notice the messages like, we have 16 land slots empty always come near the bottom of the hour, or research recommendations.
I could be entirely wrong, but it is just the feeling I get while watching the game unfold.
The bottom line is, the game has never been unplayable for me, but you are going to get some slowdown as more and more things need to be processed.
If there is a limit to the number of units allowed, I have never seen it reached.
Off topic but relevant I think.
One of the things I think could have alleviated this cycle is to have diminishing resources. Each region has a finite amount of a resource, let's take Petroleum as an example. If I start the game as the U.S.A. and I build up a massive army, more and more Petroleum is used/removed from the game. Eventually I will have none left. I am left with 3 options.
1. Reduce the size of my military
2. Try to obtain Petro on the world market
3. Take over another region with Petroleum reserves.
Now, 1 and 2 are viable options, but even they have a limited life span as eventually the worlds Petroleum would be exhausted. As each region reaches it maximum output, whereby no more may be pumped from the ground, they should start realizing from that point on it is only a matter of time. This means they would stop wanting to sell the limited amount they have left and keep it for personal use.
As the world market "dries up" more and more countries have to slow or stop unit production. This has the effect of fewer units in the game, but keeps a balance as far as individual countries are concerned.
Saudi Arabia may be leaps and bounds behind the U.S.A. in technology, but with its vast Petroleum reserves they can field a larger military. As an example.
As the game is coded now, money is the only resource you need to win. With enough of it, you can purchase anything you want because all resources are unlimited.
Sorry for the tangent.
NOTE: In game Petroleum includes Natural Gas, which I ignored for the sake of the above example.